We classify connected étale algebras
A 's in multiplicity-free modular fusion categories (MFCs)
B's at rank six, namely
rank(B)=6. There are eight MFCs in total and the result indicates that only
so(5)2 has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right
A-modules in
so(5)2. Finally, we discuss physical applications, specifically proving spontaneous
B-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models.